There is a theory in physics that says, “For every action there is an equal and opposite reaction.” In gambling, there is a similar theory. For every table game there will eventually be a side bet.
And, for every side bet there will be a Progressive version of the side bet.
The math behind progressives is probably the least understood math of any type of gambling. It really isn’t that hard once it is explained properly, but I’ve worked with a lot of inventors on a lot of progressives, and it is fairly obvious to me few people, even in the industry, understand how a progressive works mathematically.
Generally speaking there are three components of a side bet – the fixed pays, the seed and the contribution rate. Normally when we calculate the payback of a side bet, we simply multiply the fixed pays by the frequency of each winning hand and sum up these values. For a progressive, we have to alter one step slightly and add one.
For the jackpot event, we use the seed amount as the equivalent of the fixed pay for that event. Each time it is hit, the casino is on the hook to put that money back on the meter, so it is similar to a fixed pay in that regard. We then need to add the contribution rate – which is the amount of each dollar wagered that goes on the meter – to the total payback calculated.
Progressives vs. other wagers: While the top pay for most side bets is pretty large, the amount they contribute to the overall payback is usually pretty small. If you pay $1,000 for a 1-in-a-million event, the contribution rate is a meager 0.1%.
In video poker the Royal Flush contributes only 2% to the payback of the game. If we were to look at most table game sidebets, we’d probably find most top pays contribute about 1-2% (or less) to the overall payback.
When we switch to a progressive, we find the top pay frequently contributes 15-20% to the payback when we take into account both the seed and contribution rate. What does this mean for the player?
As I said, the Royal Flush accounts for 2% of the payback of video poker. What this usually means is until you hit one, you’re only playing at about 97.5%, which can be a bit rough. When you hit one, it brings the theoretical payback back to 99.5%. Hit the Royal more frequently than normal and you’re likely up money as you will be above 100%.
With progressives, it doesn’t quite work the same way. That top hand is either more rare or you’ll be playing a game that deals much more slowly than video poker, meaning there are no guarantees you will ever hit it. So, even if the side bet were paying 99.5%, like video poker, one player is going to wind up winning 15-20% of that payback and everyone else will be playing at 77.5% to 82.5%.
When you consider many side bets have paybacks far lower than 99.5%, the picture for those who don’t hit the jackpot is even bleaker. So, why do people play progressives? Two reasons: one is a bit emotional and the other a bit more practical.
First, players have always been willing to accept low paybacks for a chance to win a life-changing amount of money. The Lotto has made a lot of money for a lot of states. Most states payout only 70% on their lotteries. This is lower than the legal minimum of any casino game here in Nevada. But, for the chance, however slim, of winning millions of dollars, players are willing to throw a few dollars in for the hope of getting struck by lightning.
The second reason deals with the way progressives work and makes far more mathematical sense. To the casinos, the payback of a game is the long-term payback, which is calculated as I described earlier. You’ll note what I described completely ignores the specific value on the meter at any point in time.
This money is merely an accumulation of the contribution rate over time. It really doesn’t matter to them (mathematically) if a jackpot that is supposed to hit about once a year doesn’t get hit for 3 years. However, to the player, the payback of any wager is dependent upon the specific payouts for each winning hand at the point in which you make the wager.
It doesn’t really matter if the contribution rate is 10% or 20%. If a Jackpot that is supposed to average $250,000 goes all the way up to $600,000, then the payback at that point in time is well above the theoretical payback.
It is possible at a particular point in time that the payback of a wager could be over 100%. At this point, it makes sense to play the game mathematically. The problem is, however, it will be one person who will benefit from this occurrence and it may not be you. Then again, it might!
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].